Is it possible to wrap the original textures into the new mesh without distortion?
As long as your texture has image information for the ripped out part, you can correct the UVs by hand. One quick way to do it us by using the Pin Tool in UV Editor.

Example
I have a mesh with a hole in the middle (left). After filling the hole manually I may end up with a highly distorted, but still connected UV projection (right).



When selecting the original mesh part in Edit Mode, by default only the selcted and correctly unwrapped faces are shown in UV Image Editor. Move cursor to the UV Editor, select all vertices with A and press P to pin these vertices. This means they will not be changed if the mesh is unwrapped again.


Next select all vertices, including the newly created with distorted UVs, and unwrap using the default method (in Edit Mode: select all, U -> Unwrap; in UV Editor: select all, U)


The distorted parts are automatically repaired whilst the original parts are untouched. Optionally, press Alt+P to remove the pins again.